Magnetic sensor based on efficient spin injection into semiconductors

ABSTRACT

A magnetic sensor based on efficient spin injection of spin-polarized electrons from ferromagnets into semiconductors and rotation of electron spin under a magnetic field. Previous spin injection structures suffered from very low efficiency (less than 5). A spin injection device with a semiconductor layer sandwiched between δ-doped layers and ferromagnets allows for very high efficient (close to 100%) spin polarization to be achieved at room temperature, and allows for high magneto-sensitivity and very high operating speed, which in turn allows devising ultra fast and sensitive magnetic sensors.

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This patent document is a continuation and claims benefit of the earlier filing date of U.S. patent application Ser. No. 10/284,360, filed Oct. 31, 2002, which is hereby incorporated by reference in its entirety.

[0002] U.S. patent application Ser. No. 10/284,183, entitled “Efficient Spin Injection Into Semiconductors”, which has a common assignee and is hereby incorporated by reference in its entirety, may contain some common disclosure and may relate to the present invention.

FIELD OF THE INVENTION

[0003] This invention relates generally to spintronics. In particular, the invention relates generally to a magnetic sensor, a magnetic read nanohead, based on efficient room temperature injection of spin polarized electrons into semiconductors and rotation of their spin under action of a magnetic field.

BACKGROUND OF THE INVENTION

[0004] Over the past decade a pursuit of solid state ultra fast scaleable devices, such as magnetic sensors of nanosize proportions, based on both the charge and spin of an electron has led to a development of new fields of magnetoelectronics and spintronics. The discovery of giant magnetoresistance (GMR) in magnetic multilayers has quickly led to important applications in storage technology. GMR is a phenomenon where a relatively small change in magnetism results in a large change in the resistance of the devices.

[0005] The phenomenon of a large tunnel magnetoresistance (TMR) of ferromagnet-insulator-ferromagnet structures is a focus of product development teams in many leading companies. TMR is typically observed in F1-I-F2 structures made of two ferromagnetic layers, F1 and F2, of similar or different materials separated by the insulating thin tunnel barrier I with thickness typically ranging between 1.4-2 nm. The tunnel current through the structure may differ significantly depending on whether the magnetic moments are parallel (low resistance) or anti parallel (high resistance). For example, in ferromagnets such as Ni80Fe20, Co—Fe, and the like, resistance may differ by up to 50% at room temperature for parallel (low resistance) versus antiparallel (high resistance) moments on ferromagnetic electrodes.

[0006] It is worth mentioning recent studies of the giant ballistic magnetoresistance of Ni nanocontacts. Ballistic magnetoresistance is observed in Ni and some other nanowires where the typical cross-section the nanocontacts of the nanowire is a few square nanometers. The transport in this case is through very short constriction and it is believed to be with conservation of electron momentum (ballistic transport). The change in the contact resistance can be close to 10 fold (or about 1000%).

[0007] All magnetic sensors proposed and developed to present day, including the read heads, are based on variations of magnetic configurations, domain structures, in ferromagnets under externally applied magnetic fields. This mechanism does not ensure operating speed and sensitivity required of ultra fast sensors.

[0008] Interest has been particularly been keen on the injection of spin-polarized carriers, mainly in the form of spin-polarized electrons into semiconductors. This is large due to relatively large spin-coherence lifetime of electrons in semiconductors, possibilities for use in ultra fast devices. One such device in the works is an ultra fast and sensitive magnetic sensor such as a magnetic read head.

[0009] The possibility of spin injection from ferromagnetic semiconductors (FMS) into nonmagnetic semiconductors has been demonstrated in a number of recent publications. However, the Curie temperature (the temperature above which a material becomes non-magnetic) of magnetic semiconductors is substantially below room temperature. The low Curie temperature limits possible applications. Room-temperature spin injection from ferromagnets (FM) into semiconductors also has been demonstrated, but it remains a difficult task and the efficiency is very low. The low spin injection efficiency makes it very difficult, if not impossible, to develop an ultra fast magnetic sensor operable at room temperature.

SUMMARY OF THE INVENTION

[0010] According to an embodiment of the present invention, a magnetic sensor includes first and second ferromagnetic layers, a semiconductor layer formed between the first and second ferromagnetic layers, a first δ-doped layer formed between the first ferromagnetic layer and the semiconductor layer, and a second δ-doped layer formed between the second ferromagnetic layer and the semiconductor layer.

BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Features of the present invention will become known from the following description with reference to the drawings, in which:

[0012]FIG. 1A illustrates a density of electronic states (DOS) of ferromagnetic Ni;

[0013]FIG. 1B illustrates the density of electronic states (DOS) of ferromagnetic Ni, but at a higher resolution than in FIG. 1A;

[0014]FIG. 2A illustrates an exemplary magnetic sensor according to an embodiment of the present invention;

[0015]FIG. 2B illustrates an exemplary magnetic sensor according to another embodiment of the present invention;

[0016] FIGS. 3A1 and 3A2 illustrate an exemplary diagram of the magnetic sensors shown in FIGS. 2A and 2B at equilibrium and under bias, wherein the first and second δ-doped layers are both formed by heavily doping portions of the semiconductor layer;

[0017] FIGS. 3B1 and 3B2 illustrate an exemplary diagram of the magnetic sensors shown in FIGS. 2A and 2B at equilibrium and under bias, wherein the first and second δ-doped layers both have energy band gaps that are less than the energy band gap of the semiconductor layer;

[0018]FIGS. 4A and 4B illustrate the embodiments of magnetic sensors shown in FIGS. 2A and 2B in operation;

[0019]FIGS. 5A-5D illustrate an exemplary method of manufacturing the sensor shown in FIG. 2A; and

[0020]FIGS. 6A-6D illustrate an exemplary method of manufacturing the sensor shown in FIG. 2B.

DETAILED DESCRIPTION

[0021] For simplicity and illustrative purposes, the principles of the present invention are described by referring mainly to exemplary embodiments thereof. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention. However, the present invention may be practiced without limitation to these specific details. In other instances, well known methods and structure have not been described in detail so as not to unnecessarily obscure the present invention.

[0022] The density of states (“DOS”) is one of main characteristics of electrons in solid states, in particular, in magnetic materials, such as ferromagnetic Ni, Co, and Fe. DOS is referred to as g(E)dE), which is the number of electrons per unit volume in an energy interval (E,E+dE). FIG. 1A illustrates the DOS in ferromagnetic Ni, where arrows indicate the DOS for majority (spin up ↑) and minority (spin down ↓) electrons. Note that the DOS have high peaks for both spin-up and spin-down electrons at certain energy intervals.

[0023]FIG. 1B illustrates the density of electronic states (DOS) of ferromagnetic Ni, but at a higher resolution than in FIG. 1A. The energy origin is chosen at the Fermi level E_(F), i.e., E=E_(F)=0. As shown, there is a very large difference in the density of states of minority and majority d-electrons at E>0 (states above the Fermi level). The peak in the DOS of minority d-electron states is positioned at E=Δ₀, which for Ni, Δ₀≈0.1 eV. Similar region at E>0 exists in Co and Fe. Note that near E≈Δ₀, the DOS of the majority d-electrons and DOS of s and p electrons are all negligible when compared the DOS of minority d-electrons. Thus, if electrons are injected from the ferromagnetic material with energies E≈Δ₀, the electrons would be almost 100% polarized.

[0024]FIG. 2A illustrates an exemplary magnetic sensor 200 according to an embodiment of the present invention. As shown, the sensor 200 may include first and second ferromagnetic layers 210 and 230, respectively, and a semiconductor layer 220 formed therebetween. The sensor 200 may also include first and second δ-doped layers 215 and 225, which are located between the first ferromagnetic layer 210 and the semiconductor layer 220 and between the semiconductor layer 220 and the second ferromagnetic layer 230, respectively. The sensor 200 may further include a substrate 240, preferably a metal, formed below the first ferromagnetic layer 110.

[0025] In addition, the sensor 200 may include electrodes 260 and 250 electrically connecting, respectively, to the ferromagnetic layer 230 and the ferromagnetic layer 210 or the metal substrate 240. The electrodes 260 and 250 are not strictly necessary because the ferromagnetic layers 210 and 230 may directly play the role of electrodes.

[0026] The first and second ferromagnetic layers 210 and 230 may each be formed from various magnetic materials, preferably Ni, Fe and Co, as well as various magnetic alloys, which may include one or a combination of Fe, Co, Ni. The semiconductor layer 220 may be formed from various semiconductor materials including Si, Ge, GaAs, ZnTe, GaSb, GaP, InAs, CdSe, InP, InSb, CdTe, CdS, ZnS, ZnSe, AlP, AlAs, AlSb and also alloys and combinations of these materials. In general, it is preferred that the semiconductor layer 220 be formed from materials with relatively large time of electron spin relaxation τ_(S) (as will be shown below) such as GaAs, Ge, ZnSe and ZnCdSe. The semiconductor layer 220 is also preferred to be negatively doped.

[0027] Donor concentrations N_(d1) and N_(d2) of the first and second δ-doped layer 215 and 225 are preferred to be greater than the donor concentration N_(s) of the semiconductor layer 220, i.e., N_(d1), N_(d2)>>N_(s) should hold. In one embodiment, one or both of the first and second δ-doped layers 215 and 225 may be formed by heavily doping of portions of the semiconductor layer 220 with electron rich materials. The magnetic sensor 200 thus formed may be described as having a FM−n⁺−n−n⁺−FM structure. Examples of electron rich materials include P, As, and Sb, which are typically used to dope semiconductors Ge and Si, and Ge, Se, Te, Si, Pb and Sn, which are typically used to dope semiconductor GaAs.

[0028] The inventors have discovered that if the following conditions are satisfied, efficient spin-injection of current from the ferromagnetic layers 210 and 230 into the semiconductor layer 220 may take place at room temperature: $\begin{matrix} {{{{N_{d1}l_{+ 1}^{2}} \approx {2\frac{ɛ_{0}{ɛ\left( {\Delta - \Delta_{0}} \right)}}{q^{2}}}},{{N_{d2}l_{+ 1}^{2}} \approx {2\frac{ɛ_{0}{ɛ\left( {\Delta - \Delta_{0}} \right)}}{q^{2}}}}}\quad} & (1) \\ {{{l_{+ 1} \leq t_{0}} = \sqrt{\frac{\hslash^{2}}{2{m^{*}\left( {\Delta - \Delta_{0}} \right)}}}},{{l_{+ 2} \leq t_{0}} = \sqrt{\frac{\hslash^{2}}{2{m^{*}\left( {\Delta - \Delta_{0}} \right)}}}}} & (2) \end{matrix}$

[0029] where N_(d1) and N_(d2) represent donor concentrations of the first and second δ-doped layers 215 and 225, respectively; l₊₁ and l₊₂ represent the thicknesses of the first and second δ-doped layers 215 and 225, respectively; so represents the permittivity of free space; ε represents a relative permittivity of the semiconductor layer 220; Δ represents a height of the Schottky barrier (as measured from the Fermi level of the ferromagnetic layers 210 and 230) on the boundaries between the first ferromagnetic layer 210 and the first δ-doped layer 215 and between the second ferromagnetic layer 230 and the second δ-doped layer 225; Δ₀ represents the height of the lower and wider potential barrier in the semiconductor layer 220 (also as measured from Fermi level of the ferromagnetic layers 210 and 230); q represents elementary charge; and h is the Planck's constant. For GaAs semiconductor layer, m*≈0.07 m₀ where m₀ is the mass of free electron and t₀≈1 nm. Similarly for Si, the corresponding values are ≈0.2 m₀ and ≈0.5 nm, respectively.

[0030] Under the conditions of Equations (1) and (2), the δ-doped layers 215 and 225 become “transparent” for tunneling electrons. In other words, electrons with energy E≧Δ₀ may easily traverse the δ-doped layers 215 and 225.

[0031] As noted above, when the barrier height Δ₀ corresponds to the peak in the DOS for minority d ↓ electrons in the ferromagnetic layers 210 and 230 (see FIGS. 1A and 1B), the electrons are almost 100% polarized. In other words, P₁ and P₂ are both almost unity, where P₁ and P₂ represent degrees of polarization of injected electrons from the first ferromagnetic layer 210 to the semiconductor layer 220, the first FM-S interface, and from the second ferromagnetic layer 230 to the semiconductor layer 220, the second FM-S interface, respectively. It is preferred that the condition of Equation (1) is satisfied to the extent that a dispersion of Δ₀ is equal to the width of the peak in DOS shown in FIGS. 1A and 1B. Typically, this occurs if Equation (1) is accurate within 20 percent.

[0032] In another embodiment, one or both of the first and second δ-doped layers 215 and 225 may be formed by growing a n⁺-doped epitaxial layer on one or both sides of the n-doped semiconductor layer 220 (this structure may also be referred as a FM−n⁺−n−n⁺−FM heterostructure). It is preferred that the epitaxially grown δ-doped layers 215 and 225 be doped heavily as practicable and be as thin as practicable. Preferably, one or both of the first and second δ-doped layers 215 and 225 have a narrower energy band gap than the energy band gap of the semiconductor layer 220, i.e., E_(gδ1)<E_(g) and E_(gδ2)<E_(g), and at that electron affinities of the δ-doped layers 215 and 225 be greater than an electron affinity of the semiconductor layer 220 by a value close to Δ₀.

[0033] If one or both of the first and second δ-doped layers 215 and 225 are formed by epitaxial growth of a very thin heavily doped (i.e., n⁺ doped) and narrower energy band gap semiconductor layer, the parameters of the layers 215 and 225, i.e., their respective donor concentrations N_(d1) and N_(d2) and their thicknesses l₊₁ and l₊₂ should satisfy the following conditions for efficient spin injection: $\begin{matrix} {{N_{d1} > {2\frac{ɛ_{0}{ɛ\left( {\Delta - \Delta_{0}} \right)}}{q^{2}l_{+ 1}^{2}}}},{N_{d2} > {2\frac{ɛ_{0}{ɛ\left( {\Delta - \Delta_{0}} \right)}}{q^{2}l_{+ 2}^{2}}}}} & (3) \end{matrix}$

l ₊₁ ≦t ₀ , l ₊₂ ≦t ₀   (4)

[0034] Examples of such heterostructures include FM₁GaAs—Ga_(1-x)Al_(x)As—GaAs—FM₂ (i.e., n⁺-δ-doped layers are formed from GaAs and n-doped semiconductor layer is formed from Ga_(1-x)Al_(x)As), FM₁-Ge_(x)Si_(1-x)—Si—Ge_(x)Si_(1-x)—FM₂, and FM₁-Zn_(1-x)Cd_(x)Se—ZnSe—Zn_(1-x)Cd_(x)Se—FM₂, where x and 1-x quantities refer to the composition of the respective materials. Regarding the n⁺-δ-doped layers (e.g., GaAs, Ge_(x)Si_(1-x), and Zn_(1-x)Cd_(x)Se), their thickness l₊₁ and l₊₂ should be sufficiently thin such that corresponding FM-S interfaces become transparent for electron tunneling. The conditions of Equations (3) and (4) may be satisfied, for example, if the δ-doped layers 215 and 225 are such that the thickness l_(+1,2)≦1 nm and the donor concentration N⁺ _(d1,2)≧10²⁰ cm³.

[0035] It is possible that one of the first and second δ-doped layers 215 and 225 are formed from heavily doping a portion of the semiconductor layer 220 and the other of the first and second δ-doped layers 215 and 225 be formed by epitaxial growth.

[0036] The substrate 240 may be formed preferably from metals such as Ta, Cu, Ag, Au, and Pl. In addition, the electrodes 250 and 260 may be formed from highly conductive materials such as metals, doped silicon, and doped polysilicon.

[0037]FIG. 2B illustrates an exemplary magnetic sensor 200-2 according to another embodiment of the present invention. The sensor 200-2 is similar to the sensor 200 shown in FIG. 2A. The sensor 200-2 differs from the sensor 200 in that first and second antiferromagnetic layers 270 and 280 may be present. As shown in FIG. 2B, the first antiferromagnetic layers 270 may be placed between the first ferromagnetic layer 210 and electrode 250 and may play the role of the substrate. Similarly, the second antiferromagnetic layer 280 may be placed between the second ferromagnetic layer 230 and electrode 260. The antiferromagnetic layers 270 and 280 fix more rigidly magnetizations M₁ and M₂ within ferromagnetic layers 210 and 230, respectively. The first and second antiferromagnetic layers 270 and 280 may be formed from various materials including FeMn, IrMn, NiO, MnPt (L1₀), α-Fe₂O₃, and combinations therefrom.

[0038] FIGS. 3A1 and 3A2 illustrate an exemplary diagram of the magnetic sensor 200, 200-2 along the line II-II shown in FIGS. 2A and 2B at equilibrium (FIG. 3A1) and under bias (FIG. 3A2), wherein the first and second δ-doped layers 215 and 225 are both formed by heavily doping portions of the semiconductor layer 220.

[0039] FIGS. 3B1 and 3B2 illustrate an exemplary diagram of the magnetic sensor 200, 200-2 along the line IV-IV shown in FIGS. 2A and 2B at equilibrium (FIG. 3B1) and under bias (FIG. 3B2), wherein the first and second δ-doped layers 215 and 225 both have energy band gaps that are less than the energy band gap of the semiconductor layer 220.

[0040] With references to FIGS. 3A1-3B2, the operation of the magnetic sensors 200, 200-2 will be explained. First, under bias at room temperature, spin-polarized electrons from the first ferromagnetic layer 210 are injected into the semiconductor layer 220 through the first δ-doped layer 215 using the concept of efficient room temperature injection described above (see also below).

[0041] A potential Schottky barrier for electrons always forms at the boundary of any metal-semiconductor interface, such as at the boundary between the first ferromagnetic layer 210 and the first δ-doped layer 215. If the donor concentration N_(d1) is sufficiently high and the thickness l₊₁ is sufficiently small, the first δ-doped layer 215 is “transparent” for tunneling electrons, and the electrons from the first ferromagnetic layer 210 may easily traverse the first δ-doped layer 215.

[0042] The electrons that tunnel through the first δ-doped layer 215 meet another lower and wider potential barrier formed in the semiconductor layer 220. It is preferred that the width d of the semiconductor layer 220 be wide enough. When this occurs, electrons with energies below the barrier height are effectively filtered, and essentially, only the electrons with energies above the barrier height Δ₀ will be able to traverse the semiconductor layer 220.

[0043] It is preferred that the height of the barrier in the semiconductor layer 220 is approximately equal to E_(F)+Δ₀ where E_(F) is the Fermi level at equilibrium. Note that the potential barrier in the semiconductor layer 220 may be manipulated to a desired value by controlling the characteristics of the magnetic sensor 200, 200-2, for example by controlling the donor concentration N, of the semiconductor layer 220. As previously noted, the DOS of minority d ↓ electrons of a ferromagnet reaches maximum at energy level E≈E_(F)+Δ₀ (see FIGS. 1A and 1B). For simplicity, origin is chosen such that E_(F)=0. Then the maximum DOS of minority d ↓ electrons exceeds, by more than an order of magnitude, the DOS of other type electrons (s ↑, s ↓, p ↑, p ↓ and d ↑) in the first ferromagnetic layer 210 at E≈Δ₀.

[0044] Thus, if the potential barrier height of the semiconductor layer 220 is such that it coincides with Δ₀, then the electrons from the first ferromagnetic layer 210 tunneling through the first δ-doped layer 215 and traverse the length d of the semiconductor layer 220 will be composed of almost all minority d ↓ electrons. In other words, the injected current will be almost completely spin-polarized.

[0045] Further, the Δ₀ height of the barrier is preferred to be substantially maintained throughout the width d of the semiconductor layer 220 at equilibrium (see FIGS. 3A1 and 3B1). The height of the barrier may be substantially maintained if the donor concentration N_(s) and the width d of the semiconductor layer 220 substantially satisfy the following conditions: $\begin{matrix} {N_{s} \leq {2\frac{ɛ_{0}{ɛ\Delta}_{0}}{q^{2}d^{2}}}} & (5) \\ {{d > d_{\min}} = {{a_{B}\left( \frac{1}{k_{B}T} \right)}\sqrt{\frac{m_{0}E_{B}\Delta_{0}}{m_{e}^{*}}}}} & (6) \end{matrix}$

[0046] where a_(B)=0.05 nm and E_(B)=13.6 eV are the Bohr parameters; m₀ is mass of free electron; T is the sensor temperature and k_(B) is the Boltzmann constant. For example, d_(min)≈6 nm for GaAs and d_(min)≈3 nm for Ge when Δ₀=0.1 eV and T=300K. Under these circumstances, if d>10 nm and N_(s)≦10¹⁷ cm⁻³ the conditions specified by Equations (5) and (6) would be satisfied.

[0047] Due to the peculiarity of the DOS in the ferromagnet, the end result is that practically only the minority d ↓ electrons are injected from the first ferromagnetic layer 210 into the semiconductor layer 220. In other words, the degree of spin polarization P₁ of the injected electrons from the first ferromagnetic layer 210 into the semiconductor layer 220 is close to 1 (or close to unity). The same is true of the degree of spin polarization P₂ of electrons injected from the second ferromagnetic layer 230 into the semiconductor layer 220.

[0048] It is preferred that the electrons conserve their spin orientation during transit through the semiconductor layer 220, i.e., spin ballistic transport is desired. For spin ballistic transport to occur, a transit time τ_(d) of the electrons through of the semiconductor layer 220 of the width d should be substantially equal to or less than the spin-coherence time τ_(S) of the electrons in the semiconductor layer 220.

[0049] The transit time τ_(d) is determined by the diffusion and the drift of the electrons under the electrical field {overscore (E)} inside the semiconductor layer 220 and is equal to τ_(d)=d/v_(d) where v_(d)=μ_(n){overscore (E)}+D_(n)/d, μ_(n) and D_(n) are the mobility and the diffusion constant of the electrons. Thus, spin ballistic transport occurs when:

d<d _(max) ={square root}{square root over (D_(n)τ_(S))}  (7)

[0050] According to Equations (6) and (7), the width d of the semiconductor layer 220 should satisfy the following condition: $\begin{matrix} {{{d_{\min}{a_{B}\left( \frac{1}{k_{B}T} \right)}\sqrt{\frac{m_{0}E_{B}\Delta_{0}}{m_{e}^{*}}}} < d < d_{\max}} = \sqrt{D_{n}\tau_{S}}} & (8) \end{matrix}$

[0051] For typical parameters of Ge and GaAs, d_(min)≈10⁻⁶ cm and d_(max)≈3×10⁻³ cm.

[0052] In comparison with earlier proposed magnetic sensors, the sensors 200, 200-2 shown in FIGS. 2A and 2B possess an additional degree of freedom resulting from spin rotation of the injected spin-polarized electrons under the action of an external magnetic field during transit through the semiconductor layer 220 in the spin ballistic transport, τ_(d)≦τ_(S).

[0053] The electron spin rotation occurs with frequency ω=γH where γ=1.76×10⁷Oe⁻¹s⁻¹ is the gyromagnetic ratio and H is the magnetic field component normal to the spin (see FIG. 3A2). Thus, the angle of the spin rotation is θ_(H)=γHτ_(d) and its maximum is θH_(max)=γHτ_(S). Therefore, the total angle θ between the electron spin σ and the magnetization M₂ of the second ferromagnetic layer 230 is θ=θ₀+θ_(H) where θ₀ is the angle between the magnetizations M₁ and M₂ of the first and second ferromagnetic layers 210 and 230. The theoretical calculations and experimental studies show that the longest values for spin-coherence time τ_(S) can be realized in negative doped semiconductors (n-semiconductors) and can reach up to 1 ns in ZnSe and GaAs at room temperature. Hence it follows that θ=π can be obtained at H in several hundred Oersteds.

[0054] A conductivity G of the second FM-S interface, i.e., between the second ferromagnetic layer 230 and the semiconductor layer 220, change with the angle Θ between the electron spin σ and the magnetization M₂ of the second ferromagnetic layer 230. Note that the magnetic sensor 200-2 as shown in FIG. 2B has an advantage in that antiferromagnetic layers 270 and 280 may be used to fix magnetizations M₁ and M₂ of the first and second ferromagnetic layers 210 and 230, respectively. The conductivity G of the structures shown in FIGS. 2A and 2B may be written as:

G=G ₀(1+P ₁ P ₂ cos θ)   (9)

[0055] where P₁ and P₂ are degrees of polarizations first and second FM-S interfaces as described previously. It was also described above that the variation of the angle θ between the electron spin σ and the magnetization M₂ inside the second ferromagnetic layer 230 can exceed π when the magnetic field is several hundred Oersteds. Thus, the maximum magnetoresistance variation can reach: $\begin{matrix} {\frac{G_{\max}}{G_{\min}} = \frac{1 + {P_{1}P_{2}}}{1 - {P_{1}P_{2}}}} & (10) \end{matrix}$

[0056] As mentioned above, P₁ and P₂ for the sensors 200 and 200-2 shown in FIGS. 2A and 2B are nearly unity. Therefore, the variation of resistance of the magnetic sensor 200, 200-2 can reach several orders of magnitude. In other words, the magnetic sensors 200, 200-2 may be extremely sensitive.

[0057]FIGS. 4A and 4B illustrate the embodiments of magnetic sensors 200 and 200-2 in operation. As shown, injection of spin-polarized electrons occurs from the first ferromagnetic layer 210 into the semiconductor layer 220. The electron spin is rotated under action of a magnetic field and it causes change in resistance of the second ferromagnetic layer 230, which is measured.

[0058] The magnetic sensors 200 and 200-2 may be ultra fast. It was noted above that the transit time τ_(d) is essentially less than or equal to the spin-coherence time τ_(S) of the electrons. It was also noted above that for n-doped semiconductor 220 the spin-coherence time τ_(S) can be less than or equal to 1 ns. This means that the transit time τ_(d)<τ_(S)<1 ns. In other words, the effect of spin injection from the first ferromagnetic layer 210 and the spin rotation may manifest as a change in the resistance in the second ferromagnetic layer in less than 1 ns (or less than a billionth of a second). It should be noted that 1 ns is the maximum time at room temperature. Typically, τ_(S)=0.1-0.01 ns.

[0059]FIGS. 5A-5D illustrate an exemplary method of manufacturing the sensor 200 shown in FIG. 2A. As shown in FIG. 5A, the substrate 240 may be formed. The substrate 240 may be planarized. Then the first magnetic layer 210 may be formed on the substrate 240. Material to form the first magnetic layer 210 may be deposited, sputtered, fired on the substrate 240. The first magnetic layer 210 may also be planarized.

[0060] Then as shown in FIG. 5B, the first and second δ-doped layers 215 and 225 and the semiconductor layer 220 may be formed. In one embodiment, the first δ-doped layer 215 may be formed by epitaxial or molecular growth. The first δ-doped layer 215 may also be deposited, sputtered, or fired onto the first magnetic layer 215. Then the semiconductor layer 220 may be deposited, fired, or sputtered onto the first δ-doped layer 215. Then the second δ-doped layer 225 may be formed by epitaxial or molecular growth, or may be deposited, sputtered, or fired onto the semiconductor layer. Note that each of the first and second δ-doped layers 215 and 225 and the semiconductor layer 220 may be planarized. Also, the first and second δ-doped layers 215 and 225 may be doped more heavily as compared to the semiconductor layer 220.

[0061] In another embodiment, the semiconductor layer 220 may be formed on the first ferromagnetic layer 210 and the first and second δ-doped layers 215 and 225 may be formed by heavily doping appropriate portions of the semiconductor 220.

[0062] Then as shown in FIG. 5C, the second ferromagnetic layer 230 may be formed, again by epitaxial growth, or may be deposited, sputtered, or fired onto on the second δ-doped layer 225. The second magnetic layer 230 may be planarized.

[0063] Then as shown in FIG. 5D, the first and second electrodes 250 and 260 may be formed by sputtering, firing, or depositing materials on the first and second ferromagnetic layers 210 and 230, respectively.

[0064]FIGS. 6A-6D illustrate an exemplary method of manufacturing the sensor 200-2 shown in FIG. 2B. The method to manufacture sensor 200-2 is similar to the method illustrated in FIGS. 5A-5D. Thus the details need not be repeated. However, the methods do differ in first and second antiferromagnetic layers 270 and 270 are formed and the substrate 240 is not.

[0065] What has been described and illustrated herein are preferred embodiments of the invention along with some of its variations. The terms, descriptions, and figures used herein are set forth by way of illustration only and are not meant as limitations. Many variations are possible within the spirit and scope of the invention, which is intended to be defined by the following claims—and their equivalents—in which all terms are meant in their broadest reasonable sense unless otherwise indicated. 

What is claimed is:
 1. A magnetic sensor comprising: a first ferromagnetic layer and a second ferromagnetic layer; a semiconductor layer formed between the first and second ferromagnetic layers; a first δ-doped layer formed between the first ferromagnetic layer and the semiconductor layer; and a second δ-doped layer formed between the second ferromagnetic layer and the semiconductor layer, wherein a conductivity between the first ferromagnetic layer and the second ferromagnetic layer provides a measure of an external magnetic field that the magnetic sensor senses.
 2. The sensor of claim 1, wherein at least one of the first and second δ-doped layers is formed by doping a portion of the semiconductor layer.
 3. The sensor of claim 1, wherein the first and second δ-doped layers and the semiconductor layer are negatively doped.
 4. The sensor of claim 3, wherein the first δ-doped layer satisfies a condition ${N_{d1}l_{+ 1}^{2}} \approx {2\frac{ɛ_{0}{ɛ\left( {\Delta - \Delta_{0}} \right)}}{q^{2}}}$

and the second δ-doped layer satisfies a condition ${{N_{d2}l_{+ 1}^{2}} \approx {2\frac{ɛ_{0}{ɛ\left( {\Delta - \Delta_{0}} \right)}}{q^{2}}}},$

wherein N_(d1) and l₊₁ represent a donor concentration and a thickness of the first δ-doped layer, N_(d2) and l₊₂ represent a donor concentration and a thickness of the second δ-doped layer; q represents a positive elementary charge; ε represents a relative permittivity of the semiconductor layer, ε₀ represents a permittivity of vacuum; Δ represents a potential barrier height on interfaces between the first ferromagnetic layer and the first δ-doped layer and between the second ferromagnetic layer and the second δ-doped layer; and Δ₀ represents a height of a potential barrier formed in the semiconductor layer.
 5. The sensor of claim 4, wherein the potential barrier height Δ₀ formed in the semiconductor layer corresponds to a peak in a density of minority d ↓ electrons in at least one of the first ferromagnetic layer and the second ferromagnetic layer.
 6. The sensor of claim 5, wherein at least one of the following is true: the condition ${N_{d1}l_{+ 1}^{2}} \approx {2\frac{ɛ_{0}{ɛ\left( {\Delta - \Delta_{0}} \right)}}{q^{2}}}$

is satisfied to an extent that a dispersion of Δ₀ is substantially equal to a width of the peak in the density of states of minority d ↓ electrons of the first ferromagnetic layer; and the condition ${{N_{d2}l_{+ 1}^{2}} \approx {2\frac{ɛ_{0}{ɛ\left( {\Delta - \Delta_{0}} \right)}}{q^{2}}}},$

is satisfied to an extent that a dispersion of Δ₀ is substantially equal to a width of the peak in the density of states of minority d ↓ electrons of the second ferromagnetic layer.
 7. The sensor of claim 4, wherein at least one of the following is true: the thickness l₊₁ of the first δ-doped layer is less than or substantially equal to 1 nanometer and the donor concentration of N_(d1) of the first δ-doped layer substantially ranges from 10²⁰ cm⁻³ to 10²¹ cm⁻³; and the thickness l₊₂ of the second δ-doped layer is less than or substantially equal to 1 nanometer and the donor concentration of N_(d2) of the second δ-doped layer substantially ranges from 10²⁰ cm⁻³ to 10²¹ cm⁻³.
 8. The sensor of claim 1, wherein at least one of the first and second ferromagnetic layers is formed from at least one of Ni, Fe, Co, and alloys there of.
 9. The sensor of claim 1, wherein the semiconductor layer is formed from at least one of Si, GaAs, ZnTe, GaSb, GaP, Ge, InAs, CdSe, InP, InSb, CdTe, CdS, ZnS, ZnSe, AlP, AlAs, and AlSb.
 10. The sensor of claim 1, wherein at least one of an energy band gap of the first and second δ-doped layers is narrower than an energy band gap of the semiconductor layer.
 11. The sensor of claim 10, wherein: at least one of the first and second δ-doped layers is formed from at least one of GaAs, Ge_(x)Si_(1-x), In_(x)Ga_(1-x)As, and Zn_(1-x)Cd_(x)Se; and the semiconductor layer is formed from at least one of GaAs, Si, In_(x)Ga_(1-x)As, and ZnSe.
 12. The sensor of claim 1, further comprising: a first electrode connecting to the first ferromagnetic layer; and a second electrode electrically connecting to the second ferromagnetic layer.
 13. A magnetic sensor comprising: a first magnetized layer; a second magnetized layer; and a semiconductor layer formed between the first and second magnetized layers, wherein a conductivity between the first magnetized layer and the second magnetized layer provides a measure of an external magnetic field that the magnetic sensor senses.
 14. The sensor of claim 13, wherein each of the first and second magnetized layers comprises a ferromagnetic material.
 15. The sensor of claim 13, wherein a first magnetization of the first magnetized layer and a second magnetization of the second magnetized layer are fixed, and the conductivity depends on an amount of spin rotation that the external magnetic field causes for spin-polarized electrons that are injected from the first magnetized layer through the semiconductor layer into the second magnetized layer.
 16. The sensor of claim 13, further comprising a first δ-doped layer between the first magnetized layer and the semiconductor layer, wherein the first δ-doped layer improves efficiency of injection the spin-polarized electrons through an interface between the first magnetized layer and the semiconductor layer.
 17. The sensor of claim 16, further comprising a second δ-doped layer between the semiconductor layer and the second magnetized layer, wherein the second δ-doped layers improve efficiency of injection the spin-polarized electrons through an interface between the semiconductor layer and the second magnetized layer.
 18. The sensor of claim 13, wherein the semiconductor layer has a width d satisfying ${{{a_{B}\left( \frac{1}{k_{B}T} \right)}\sqrt{\frac{m_{0}E_{B}\Delta_{0}}{m_{e}^{*}}}} < d < \sqrt{D_{n}\tau_{S}}},$

where a_(B) and E_(B) are Bohr parameters and are respectively about 0.05 nm and about 13.6 eV; m₀ is the mass of a free electron; k_(B) is the Boltzmann constant, T is a temperature of the sensor, Δ₀ is a height of a potential barrier formed in the semiconductor layer, m_(e)* is an effective mass of an electron in the semiconductor layer, D_(n) is a diffusion constant for electrons in the semiconductor layer, and τ_(S) is a spin-relaxation time of electrons in the semiconductor layer.
 19. The sensor of claim 13, where the semiconductor layer has a donor concentration that is less than 10¹⁷ cm⁻³. 